Bézier Curves and Surfaces Based on Modified Bernstein Polynomials.

In this paper, Bézier curves and surfaces have been constructed based on modified Bernstein bases functions with shifted knots for t ϵ [α/ n+β , n+α / n+β ] . Various prop- erties of these modified Bernstein bases are studied. A de Casteljau type algorithm has been developed to compute Bézier curves and surfaces with shifted knots. Furthermore, some fundamental properties of Bézier curves and surfaces with modified Bernstein bases are also discussed. Introduction of parameters α and β enable us to shift Bernstein bases functions over subintervals of [0; 1]. These new curves have some properties similar to classical Bézier curves. We get Bézier curves defined on [0; 1] when we set the parameters α; β to the value 0: Simulation study is performed through MATLAB R2010a. It has been concluded that Bézier curves that are generated over any subinterval of [0; 1] based on modified Bernstein bases functions are similar to the Bézier curves that are generated based on classical Bernstein bases functions over the interval [0; 1]. [ABSTRACT FROM AUTHOR]